Názov:The Cycle Double Cover Conjecture and Related Conjectures
Vedúci:doc. RNDr. Edita Mačajová, PhD.
Kµúčové slová:The Cycle Double Cover Conjecture, CDC, induced cycle, cubic graphs, snark
Abstrakt:In this thesis, we pursue our own conjecture regarding cycle double covers. Firstly, we provide important definitions we use throughout the thesis, as well as observations and known facts about cycle double covers. Later, we state the new facts we discovered about $2$-edge cuts, nontrivial $3$-edge cuts, and triangles with regard to cycle double covers. We also state our conjecture and provide proofs of our conjecture for some infinite graph families such as Issacs snarks. Lastly, we describe implementation details of our software, including how we represented graphs, the algorithm we used for finding cycle double covers in addition to some methods that helped us to find the cycle double covers that we used in proofs of our conjecture.

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